Abstract Extratropical cyclones strongly influence Arctic sea ice thermodynamics through episodic heat and moisture transport, yet their thickness‐dependent impacts remain poorly quantified. Using comprehensive observations from the Multidisciplinary Drifting Observatory for the Study of Arctic Climate (MOSAiC), we investigate how sea ice thickness (SIT) regulates thermodynamic responses during cyclones. Cyclone‐induced atmospheric perturbations propagate downward through the ice, and anomalies in conductive (Fc ${F}{c}$), sensible (Fs ${F}{s}$), latent (Fl ${F}{l}$), and oceanic (Fw ${F}{w}$) heat fluxes at base all decrease with increasing SIT, indicating stronger responses in thinner ice. Among them, Fc ${F}{c}$ exhibits the strongest sensitivity to SIT, followed by Fs ${F}{s}$, whereas Fl ${F}{l}$ and Fw ${F}{w}$ show weaker dependence because synoptic signals are progressively damped during downward propagation. These sensitivities are closely related to cyclone timing and intensity. Although cyclones exert limited immediate influence on basal ice growth, their cumulative effect during the ice growth season produces net warming of the ice, potentially favoring earlier melt onset.